The Economics of Information

Risk a situation in which there is a probability that an event will occur. People tend to prefer greater certainty and less risk.

Probability A number between 0 and 1 that measures the chance that an event will occur. If probability = 0, the event will definitely not occur. If probability = 1, the event will definitely occur. If probability = 0.5, the event is just as likely to occur as not. Example: The probability that a fair (balanced coin) will land heads is 0.5.

Wealth (thousands of dollars) Total Utility TU As wealth increases, so does the total utility of wealth. But the marginal utility of wealth diminishes. In other words, the slope of the total utility curve is positive but decreasing.

When there is uncertainty, people do not know the actual utility they will get from taking a particular action. They do know the utility they expect to get. Expected utility is the average utility of all possible outcomes.

Expected Value Suppose you have a generous but forgetful aunt. There is a 50% probability that she will remember your birthday and send you a check for $100. There is also a 50% probability that she will forget your birthday and send you nothing. What is the expected value of the gift (G) you will receive from your aunt for your birthday? E(G) = 0.5 (0) (100) = 50.

E(X) = p 1 X 1 + p 2 X 2 + p 3 X 3 + … + p k X k So to calculate the expected value, you take the amount of each possible outcome, multiply it by the probability of that outcome, and add the products together.

Apart from concerns about your aunt’s health, would you rather have your aunt send a $50 check with certainty over the current situation? If the answer is yes, you are risk averse. If you prefer the current situation, you are risk loving. If you are indifferent between the two situations, you are risk neutral.

In general, A risk-neutral person cares only about expected wealth and doesn’t care how much uncertainty there is. A risk-averse person prefers the expected wealth with certainty over the risky situation with the same expected wealth. A risk-loving person enjoys the thrill of the gamble, and so prefers the risky situation over a situation with the same expected wealth with certainty. Most people are risk averse, but some people are more risk averse than others.

The shape of the utility-of-wealth curve tells us about the person’s degree of risk aversion. Wealth (thousands of dollars) Total Utility Person 1 The more rapidly the slope of the TU curve falls, the more risk averse the person is. The slope of the TU curve of person 3 drops the fastest, so that person is the most risk averse. Person 2 Person 3

Example: Alex is considering a job, which is based on commission, & pays $3000 with 50% probability & $9000 with 50% probability. Wealth (thousands of dollars) Total Utility $3000 is worth 65 units of utility to Alex, and $9000 is worth 95 units of utility. The utility of the job’s earnings is the average of 65 & 95, or 80 units of utility. We can see from the TU curve that a job paying $6000 with certainty would be worth more to Alex (85 units of utility). A job that paid $5000 with certainty would be worth the same level of utility to Alex as the risky job

For a risk-neutral person the TU curve would be linear, instead of concave. For a risk-lover, the TU curve would be convex.

Insurance Insurance works by pooling risks. It is profitable because people are risk averse.

Example: Beth’s only wealth is a $10,000 car. Wealth (thousands of dollars) Total Utility If she doesn’t have an accident, her utility is 100 units. If she has an accident that totals her car, her utility is 0 units. (Assume there are no other options.)

Wealth (thousands of dollars) Total Utility Her expected utility is 100   0.1 = 90 units. Beth would also have 90 units of utility if her wealth was $7000 with certainty. Suppose the probability that Beth will have an accident is Without insurance, Beth’s expected wealth is $10,000  $0  0.1 = $9000.

Wealth (thousands of dollars) Total Utility So she would buy the insurance if it cost less than $3000. If insurance would pay her the money to replace her car, and the insurance cost $3000, she would have $10,000 – $3000 = $7000 with certainty.

If there are many people like Beth, each with a $10,000 car and each with a 10 percent chance of having an accident, an insurance company pays out $1,000 per person on the average, which is less than Beth’s willingness to pay for insurance.

Searching for Price Information When many firms sell the same item, there is a range of prices and buyers try to find the lowest price. But searching for a lower price is costly. Buyers balance the expected gain from further search against the cost of further search.

Optimal Search Rule Search for a lower price until the expected marginal benefit of additional search equals the marginal cost of search. When the expected marginal benefit from additional search is less than or equal to the marginal cost, stop searching and buy.

Benefits & Costs of Search Lowest price found (thousands of dollars) Benefits & Costs of Search MC MB The red line is the marginal cost of visiting one more dealer. The green line is the expected marginal benefit of visiting one more dealer. The MB is declining because the lower the best price you’ve found so far, the lower the expected marginal benefit of visiting one more dealer.

The price at which expected marginal benefit equals marginal cost is your reservation price. Lowest price found (thousands of dollars) Benefits & Costs of Search If you find a price that is greater than your reservation price, you keep searching. If you find a price equal to or below your reservation price, you stop searching and buy. In this example, the reservation price is $15,000. MC MB

Two Types of Information Problems –1. Moral hazard –2. Adverse selection

Moral hazard when one of the parties to an agreement has an incentive after the agreement is made to act in a manner that brings additional benefits to himself or herself at the expense of the other party. Example: As a result of having insurance, an individual may be more likely to engage in risky behavior.

A market response to moral hazard The insured person is required to pay part of the costs. This is coinsurance. In addition to lowering the costs of insurance directly, coinsurance gives the insured person the incentive to be economical.

Adverse selection the tendency for people to enter into agreements in which they can use their private information to their advantage and to the disadvantage of the less informed party. Example 1: Sellers may be more likely to sell low-quality goods. Example 2: Higher-risk customers may be more likely to purchase.

A case of adverse selection: The Lemon Problem Suppose a defective used car (lemon) is worth $2,000. A used car without defects is worth $8,000. Only the current owner or dealer knows if a car is a lemon. A buyer only knows it’s a lemon after buying it. Because buyers can’t tell the difference between a lemon and a good car, the price they are willing to pay for a used car reflects the fact that the car might be a lemon.

Suppose 25% of the used cars are lemons. Then a buyer would only be willing to purchase a car for 0.75 x x 2000 = $6500. At this price, fewer cars are supplied to the market. Furthermore, the number of good cars is likely to drop more than the number of lemons, so the proportion of defective cars will probably be higher. The buyers would then adjust the price they are willing to pay downward. This process could continue until the good cars are driven out of the market.

A Market Response to the Lemon Problem: Warranties –To convince a buyer that it is worth paying $8000, the dealer offers a warranty. –The dealer signals which cars are good ones and which are lemons.

Another way that the market deals with adverse selection is that companies sometimes use indirect measures to help identify high-risk customers. For example, young men have more accidents than women and older men, so insurance companies charge them a higher rate. In making loans, banks use signals such as length of time in a job, ownership of a home, marital status, and age as indicators of people who may be more likely to default on a loan.

Managing Risk in Financial Markets –To cope with risky investments such as stocks & bonds, people diversify their asset holdings. –How does diversification reduce risk?

Example Suppose you can invest $100,000 in one of two projects. Suppose also that the 2 projects are independent, so the outcome of one project is unrelated to the outcome of the other. Both investments have a 50% probability of a $50,000 profit & a 50% probability of a $25,000 loss. So the expected return on each project is ($50,000  0.5) + (–$25,000  0.5) = $12,500.

Undiversified Invest $100,000 in either project. Your expected return is $12,500. But there is no chance that you will actually make a return of $12,500. You either earn $50,000 or lose $25,000.

Diversified Invest 50% of your money in Project 1 & 50% in Project 2. $50,000 invested in a project results in a 50% chance of a 25,000 profit & a 50% chance of a 12,500 loss from that project. You now have 4 possible returns with a 25% chance each: (1) Lose $12,500 on each project, a loss of $25,000. (2) Make a profit of $25,000 on Project 1 and lose $12,500 on Project 2, a return of $12,500. (3) Lose $12,500 on Project 1 and make a profit of $25,000 on Project 2, again a return of $12,500. (4) Make a profit of $25,000 on each project, and your return is $50,000. Your expected return is now (–25,000  0.25) + (12,500  0.25) + (12,500  0.25) + (50,000  0.25) = –6, , , ,500 = $12,500. You still have an expected return of $12,500.

But… You have lowered the chance that you will earn $50,000 from 0.50 to You have lowered the chance that you will lose $25,000 from 0.50 to And you have increased the chance that you will earn your expected return of $12,500 from 0 to 0.50.